65/71 Additive Inverse :
The additive inverse of 65/71 is -65/71.
This means that when we add 65/71 and -65/71, the result is zero:
65/71 + (-65/71) = 0
Additive Inverse of a Fraction
For fractions, the additive inverse is found by negating the numerator or denominator, but not both. In this case:
- Original fraction: 65/71
- Additive inverse: -65/71
To verify: 65/71 + (-65/71) = 0
Extended Mathematical Exploration of 65/71
Let's explore various mathematical operations and concepts related to 65/71 and its additive inverse -65/71.
Basic Operations and Properties
- Square of 65/71: 0.8381273556834
- Cube of 65/71: 0.76729969182283
- Square root of |65/71|: 0.9568139619312
- Reciprocal of 65/71: 1.0923076923077
- Double of 65/71: 1.830985915493
- Half of 65/71: 0.45774647887324
- Absolute value of 65/71: 0.91549295774648
Trigonometric Functions
- Sine of 65/71: 0.79286309155131
- Cosine of 65/71: 0.60939980148971
- Tangent of 65/71: 1.3010557102466
Exponential and Logarithmic Functions
- e^65/71: 2.4980063600237
- Natural log of 65/71: -0.088292607145678
Floor and Ceiling Functions
- Floor of 65/71: 0
- Ceiling of 65/71: 1
Interesting Properties and Relationships
- The sum of 65/71 and its additive inverse (-65/71) is always 0.
- The product of 65/71 and its additive inverse is: -4225
- The average of 65/71 and its additive inverse is always 0.
- The distance between 65/71 and its additive inverse on a number line is: 130
Applications in Algebra
Consider the equation: x + 65/71 = 0
The solution to this equation is x = -65/71, which is the additive inverse of 65/71.
Graphical Representation
On a coordinate plane:
- The point (65/71, 0) is reflected across the y-axis to (-65/71, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 65/71 and Its Additive Inverse
Consider the alternating series: 65/71 + (-65/71) + 65/71 + (-65/71) + ...
The sum of this series oscillates between 0 and 65/71, never converging unless 65/71 is 0.
In Number Theory
For integer values:
- If 65/71 is even, its additive inverse is also even.
- If 65/71 is odd, its additive inverse is also odd.
- The sum of the digits of 65/71 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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